1. Technical Field
The disclosure relates in general to a resonator, and more particularly to a resonator having a periodic structure.
2. Description of the Related Art
The micro electro mechanical system (MEMS) technology is to manufacture an electronic mechanical mechanism element on a silicon wafer substrate to implement the functions that cannot be conventionally obtained.
With the globalization of economic development and the requirements in the mobile and wireless multimedia communication, various wireless communication systems, such as Global System for Mobile Communications (GSM), Bluetooth, wireless local area network (WLAN), 3rd-generation (3G) of mobile communication technology, Worldwide Interoperability for Microwave Access (WiMAX), have been developed flourishingly in the past few years. At present, there are more than seven standards or bands applied to the wireless communication, wherein the standards respectively have their unique communication protocols, such as different bands, different channel bandwidths, and the like. In order to achieve the seamless communication connection, the future mobile phones adopt tunable high-frequency front-end modules to perform the settings according to different communication systems so that the reconfigurable system architecture can be implemented.
After the wireless communication system is developed toward the high frequency trend, the miniaturized, low-cost, modularized, monolithic high-frequency circuits manufactured on the silicon wafer substrate using the MEMS element manufacturing technology will play an important role in the future.
The loss of the conventional radio frequency element is increased with the increase of the frequency because the conductor and the medium are at the gigahertz (GHz) frequency. Thus, the film bulk acoustic-wave resonator (FBAR) working by way of mechanism resonance has gradually replaced the associated elements and thus become the main element of the filter for the mobile phone because it advantageously has the large size and the high quality factor (Q factor). However, the currently commercial film bulk acoustic-wave resonance filter has the quality factor Q ranging from about 800 to 1200 at 1 GHz and is only suitable for serving as a band selective filter. If a “channel selective filter” has to be developed to satisfy the next generation tunable channel selective high-frequency front-end module, the quality factor Q of the radio frequency MEMS resonator (RF MEMS resonator) has to be greater than or equal to 10,000 at 1 GHz. Thus, it is a major challenge to the international researchers and developers to design a resonator with the extremely high quality factor Q and thus to achieve the target of the channel selective filter.
Regarding to how to increase the product of frequency-quality factor (f-Q), the international research and development units presently aim at the target regarding how to lower the loss of the resonator within one resonance period. At present, the known loss mechanism of the resonating body may be obtained from the following equation:
            1      Q        ≅                  1                  Q          air                    +              1                  Q          TED                    +              1                  Q          support                    +              1                  Q          surface                      ,
wherein:
Qair represents the air damping;
QTED represents the thermoelastic damping (TED);
Qsupport represents the support loss; and
Qsurface represents the surface loss.
In general, the loss item of air damping may be neglected in a system under vacuum (or low pressure) condition, and the surface loss in the mechanical structure resonator may also be neglected. So, the most important issue is to consider the two factors including the thermoelastic damping (TED) and the support loss. The main loss of the two factors in the high-frequency MEMS structure relates to the frequency. Some people have disclosed that the support loss will be the main reason of disabling the quality factor Q of the resonator Q from being increased at the high frequency (>100 MHz) in some references (theoretical and experimental references). Therefore, some academic institutions and MEMS manufacturers have devoted themselves to the analysis and computation of the support loss and disclosed various patented techniques to prevent the elastic waves from propagating to the substrate through the support beam and thus to increase the quality factor Q.
In a conventional resonator structure, the resonating body is mounted on the substrate using the support beam, and the resonating body, the support beam and the substrate are made of the same material, such as silicon, and thus have the same acoustic impedance (see Equation (1)). The vibration energy can be transferred on the same material more easily. Thus, after the elastic waves of the resonating body propagate to the support beam, the elastic waves are substantially completely (close to 100%) lost on the substrate without reflection.
                    Z        =                  ρ          *                                    E              ρ                                                          (        1        )            
Two different patented techniques are disclosed in the following, and the technical contents thereof are to prevent the elastic waves from propagating to the substrate through the support beam so that the loss can be reduced and the quality factor Q can be increased.
U.S. Pat. No. 6,628,177 (hereinafter referred to as '177 patent) entitled “Micromechanical resonator device and micromechanical device utilizing same” discloses an MEMS resonating element, as shown in FIG. 1. Regarding the technical means of the '177 patent, a diamond film is grown into a body of a disk resonator, the acoustic wave impedances of diamond and silicon are different from each other and are respectively 6.18*107 Kg/m2/s and 1.85*107 Kg/m2/s. Thus, an elastic wave reflecting surface is formed to reflect the body waves back to the resonating body to form a high quality factor (High-Q) resonator. The resonator structure of FIG. 1 mainly includes a diamond disk resonating body (diamond disk) 101, a polysilicon stem 102 and a nodal ring 104. When the acoustic wave reaches an interface 105 between the diamond and the silicon, it is reflected back to the resonating body. Thus, the interface 105 also serves as the acoustic wave reflecting surface. The diamond is the surface reflecting material having the maximum acoustic wave impedance in the nature.
The experimental data of '177 patent is also disclosed in IEEE journal in 2004, as shown in the following Table 1. As shown in Table 1, it is obtained that the quality factor Q of the disk resonator with the diamond film may be significantly increased by more than six times (55300/8100≅6.83).
TABLE 1StemRes.ModuleStemDiskDiam.,DiskFreg.,Quality(Mode)materialmaterialμmDiam., μmMHzFactor QFirstSiliconSilicon1.622.0245.18,100ModuleFirstSiliconDiamond1.622.0497.5855,300module
An elastic wave reflecting surface for reflecting energy may be generated using different materials, and the use of the diamond film can handle all the bandwidths.
Another U.S. Pat. No. 7,295,088 (hereinafter referred to as '088 patent) entitled “High-Q micromechanical resonator devices and filters utilizing same” discloses another MEMS resonating element, as shown in FIG. 2. The MEMS resonating element mainly includes an annular resonating body 201, a middle anchor 202 and a cruciform support beam 203. The annular resonating body 201 has a central cavity, and the middle anchor 202 is disposed at a central location of the central cavity of the annular resonating body 201. The cruciform support beam 203 outwardly and radially connected to an inner ring of the annular resonating body 201 from the middle anchor 202 to support the resonating body 201. The external side and the internal side of the annular resonating body 201 are respectively formed with a sense electrode 205 and a drive electrode 206, and the electrodes overlap with each other so that the overall support structure cannot be easily interfered and the high quality factor Q and the low impedance can be obtained.
Unlike the '177 patent, in which two different materials of the diamond and the silicon are adopted, the '088 patent discloses the following features. Under the same material parameter (i.e., the resonating body 201, the middle anchor 202 and the cruciform support beam 203 are made of the same material), the cruciform support beam 203 is connected to the substrate, and this may be regarded as the completely short-circuited (i.e., the impedances completely match). However, when the length of the cruciform support beam 203 is gradually increased to the quarter-wavelength, the impedances have the maximum mismatch because one end has the maximum deformation while the other end has the minimum deformation. So, the maximum energy may be reflected back to the resonating body 201. Thus, the main technological feature of the '088 patent is that: when the length of the cruciform support beam 203 is equal to the quarter-wavelength or (2n+1) times of the wavelength, the resonating element of FIG. 2 has the highest quality factor Q (Q is equal to about 14,643 at the frequency of 1.2 GHz).